Muon Intensity Research Articles

Angular distributions of atmospheric cosmic muons at the Earth: A study with PYTHIA8

In this work, the angular distribution of atmospheric cosmic muons is studied using PYTHIA8 simulations, comparing it to the experimental data. The standalone code in PYTHIA8 consists of an atmosphere of only nitrogen molecules. Here, the standalone code has been augmented adding oxygen molecules with a relative abundance of 78:22 (Nitrogen:Oxygen) to resemble a more realistic atmosphere. The vertical flux intensity ([Formula: see text]) of cosmic muons varies with zenith angle as a function of [Formula: see text], where [Formula: see text] is the zenith angle and n is the exponent term. The vertical flux intensity of cosmic muons has been characterized as a function of zenith angle ([Formula: see text]), momentum (p) and energy (E). Simulations are compared to the experimental results found in the literature and to the measurements performed at the surface laboratories of SINP (Kolkata) and JUSL (Jadugoda) at two different latitudes and altitudes in May 2024. The integrated vertical muon flux ([Formula: see text]) and the exponent term (n) are extracted by fitting each experimental dataset. The simulated vertical flux intensity ([Formula: see text]) as a function of the zenith angle ([Formula: see text]) of cosmic muons shows a good level of agreement with the spectral shape of our experimental data as well as with that from literature. This study highlights the relevance of PYHTIA8 in the context of air-shower simulations, improving its predictive power by incorporating a more realistic atmospheric model.

Proposed Peking University muon experiment for muon tomography and dark matter search

A set of new methods are proposed here to directly detect light mass dark matter through its scattering with abundant atmospheric muons or accelerator beams. A first plan is to use the free cosmic-ray muons interacting with dark matter in a volume surrounded by tracking detectors, to trace the possible interaction between dark matter and muons. Secondly, the same device can be interfaced with domestic or international muon beams. Due to the much larger muon intensity and focused beam, it is anticipated that the detector can be made further compact, and the resulting sensitivity on dark matter searches will be improved. Furthermore, it may also be possible to measure precisely directional distributions of cosmic-ray muons, either at mountain or sea level, and the differences may reveal possible information about dark matter distributed near the Earth. Specifically, methods described here can have advantages over “exotic” dark matters that are either muonphilic or slowed down due to some mechanism, and the sensitivity on dark matter and muon scattering cross section can reach as low as microbarn level. Published by the American Physical Society 2024

Observation of thunderstorm-induced muon events in GRAPES-3 experiment

The GRAPES-3 tracking muon telescope located at Ooty (India) records short-term variations in the muon intensity during major thunderstorms, termed thunderstorm-induced muon events (TIMEs). Its excellent angular resolution, coupled with high statistics, allows us to observe subtle directional variations in muon rate. We detected 169 statistically significant events during the five-year period from 2006 through 2010. The monthly and seasonal variation patterns of the observed TIMEs were discussed, emphasizing their occurrence and climatological aspects. The annual diurnal pattern was plotted with the Carnegie curve, considering their possible causal link with the global electric circuit. The work represents the first report from any experiment for such an extended period in an uninterrupted manner.

The 48-Year Data Analysis Collected by Nagoya Muon Telescope—A Detection of Possible (125 ± 45) Day Periodicity

Muons produced by cosmic rays above the atmosphere provide valuable information on the intensity of cosmic rays and variations in the upper atmosphere. Since 1970, the Nagoya University Cosmic Ray Laboratory has been observing the muon intensity using a multi-directional cosmic ray telescope with two layers of 36 plastic scintillators of 1m2 each, which measure the muon intensity in different incident directions. The energy of an incident proton that produces a muon incident from a vertical direction is over 11.5 GV. This paper analyzes vertical muon intensities obtained over 48 years from 1970 to 2018 using methods that differ from the East–West method. As a result, a new periodicity of (125±45) days and a new periodicity of (4–16) days were found. The latter appears only in winter time, so it may be caused by a synoptic-scale disturbance associated with the arrival of the Siberian cold air mass. On the other hand, the former periodicity may be related to solar dynamo activity. In 1984, the Solar Maximum Mission’s Gamma Ray Spectrometers reported a periodicity of about (154±10) days in the flux of solar gamma rays. The (125±45)-day periodicity found here is most likely related to solar dynamo activity, since the intensity of cosmic rays around 11.5 GV is affected by the magnetic field induced by the Sun. However, this (125±45)-day periodicity differs from the report measured by the GRS instrument in a point that it also appears during periods of low solar activity. Furthermore, it has not appeared often during lower solar activity since 1992. This information is important for future investigation of the origin of this periodicity.

Intensity measurement of the surface muon beam of MELODY

A Muon station for science, technology and industry project will be constructed at China Spallation Neutron Source. The Phase I project will provide a surface muon beam with a pulse width of 130 ns at a rate over 105 µ+/pulse. Beam intensity is the key design parameter of this project. Accurate measurement of the intensity is also essential for the calibration of the µSR spectrometer. The key to the surface muon intensity measurement is to distinguish background positrons from muons. A double-stacked scintillator detector based on PMT readout scheme has been proposed, which can determine the intensity of muons and background positrons by using pulse shape discrimination method. Detailed description of the detector principle and simulated results will be presented.

Correction of the Temperature Effect of Muon Counts Observed at the Guangzhou Station

Muons are the main component of secondary cosmic rays, and the variation in muon intensity indicates the variation in primary cosmic ray intensity. However, before using muons to study the variation in the intensity of cosmic rays, it is necessary to eliminate the atmospheric effects, such as pressure and temperature effects. In this work, the temperature effect of the muons is corrected in terms of empirical method by using ground temperature. The temperature correction is applied to the muon data observed at the Guangzhou station during the period 2010–2021 after a barometric correction. It is found that the effect of seasonal variations in temperature on muon counts is greatly eliminated in the corrected data. Furthermore, the muon data are well correlated with the neutron data in comparison, which verifies the reliability of the corrected muon data. Our results show that the correction of muon data by using ground temperature is an effective method.

Beamline design and optimisation for high intensity muon beams at PSI

The High Intensity Muon Beams (HIMB) project at the Paul Scherrer Institute (PSI) will provide muon intensities of the order of 1010 muons/s for particle physics and material science experiments, two orders of magnitude higher than the state of the art, which is currently available also at PSI. In particle transport simulations for the HIMB, we use G4beamline with measured + cross-sections and with variance reduction. We also use the codes COSY INFINITY, TRANSPORT, and TURTLE for some studies. We perform asynchronous Bayesian optimisation of the beamlines on a computing cluster using G4beamline and the optimisation package DeepHyper. We performed numerous studies for the design of the HIMB, and we produced various results, including the muon transmission, beam phase space, polarisation, and momentum spectrum.

Joint inversion of muon tomography and gravity gradiometry for improved monitoring of steam‐assisted gravity drainage reservoirs

ABSTRACTSteam‐assisted gravity drainage reservoirs require an immense amount of energy and water resources, and proper monitoring of steam evolution and depletion patterns is integral to the economic and environmental efficiency of the operation. Muon tomography is a passive sensing technique, which has proven to successfully model density anomalies in a variety of applications but has not yet been applied to the oil and gas field. A previous study simulated muon intensity data to model density changes in a realistic steam‐assisted gravity drainage reservoir at 1.25 and 5 years after initial production. The results showed that muon tomography is a promising technique for monitoring steam‐assisted gravity drainage reservoirs with high spatial resolution and over short time intervals of weeks to months. Here we demonstrate the advantage of using vertical gravity gradient data and muon tomography data in a joint inversion to improve the muon‐only inverse models. Forward models for simulated muon and gravity gradient data are jointly inverted for a realistic steam‐assisted gravity drainage reservoir at 230 and 130 m total vertical depth at 1.25 years after initial production. Results show that the addition of gravity gradient data helps to constrain the density change models mainly in depth and to a smaller extent laterally. For a sparse muon sensor array of 48 sensors over a reservoir at depth, the joint inversion using gravity gradient data reduces the difference between the inverse and true model by 12% compared to a muon‐only inversion. The improvement is smaller at depth with 6%. The improvement in resolvability metrics is summarized, and limitations are discussed. The addition of multiple data types in a joint inversion improves the resulting models leading to an overall decrease in model uncertainty which can be used for improved operational efficiency in steam‐assisted gravity drainage operations.

On the Accuracy of Underground Muon Intensity Calculations

Abstract Cosmic-ray muons detected by deep underground and underwater detectors have served as an information source on the high-energy cosmic-ray spectrum and hadronic interactions in air showers for almost a century. The theoretical interest in underground muons has nearly faded away because space-borne experiments probe the cosmic-ray spectrum more directly, and accelerators provide precise measurements of hadron yields. However, underground muons probe unique hadron interaction energies and phase space, which are still inaccessible to present accelerator experiments. The cosmic-ray nucleon energies reach the hundred-TeV and PeV ranges, which are barely accessible with space-borne experiments. Our new calculation combines two modern computational tools: mceq for surface muon fluxes and proposal for underground transport. We demonstrate excellent agreement with measurements of cosmic-ray muon intensities underground within estimated errors. Beyond that, the precision of historical data turns out to be significantly smaller than our error estimates. This result shows that the sources of high-energy atmospheric lepton flux uncertainties at the surface or underground can be significantly constrained without taking more data or building new detectors. The reduction of uncertainties can be expected to impact data analyses at large-volume neutrino telescopes and be used for the design of future ton-scale direct dark matter detectors.

Towards a New μ→eγ Search with the MEG II Experiment: From Design to Commissioning

The MEG experiment represents the state of the art in the search for the Charged Lepton Flavour Violating μ+→e+γ decay. With its first phase of operations at the Paul Scherrer Institut (PSI), MEG set the most stringent upper limit on the BR (μ+→e+γ)≤4.2×10−13 at 90% confidence level, imposing one of the tightest constraints on models predicting LFV-enhancements through new physics beyond the Standard Model. An upgrade of the MEG experiment, MEG II, was designed and it is presently in the commissioning phase, aiming at a sensitivity level of 6×10−14. The MEG II experiment relies on a series of upgrades, which include an improvement of the photon detector resolutions, brand new detectors on the positron side with better acceptance, efficiency and performances and new and optimized trigger and DAQ electronics to exploit a muon beam intensity twice as high as that of MEG (7×107 μ+/s). This paper presents a complete overview of the MEG II experimental apparatus and the current status of the detector commissioning in view of the physics data taking in the upcoming three years.

Controlling the process of muon formation for muon-catalyzed fusion: method of non-destructive average muon sign detection

The recent development of intense muon sources (Holmlid, Swedish Patent SE 539,684 C 2 (2017)) is crucial for the use of muon-catalyzed fusion reactors (L. Holmlid, Fusion Science and Technology 75, 208 (2019)) which are likely to be the first generation of practical fusion reactors. For this purpose, only negative muons are useful. For existing sources where negative muons can be ejected (if not formed) preferentially, it is necessary to know the amount of negative muons to determine and optimize the fusion reactor efficiency on-line. Here, a method is developed to measure the absolute muon flux and its average sign without collecting or deflecting the muons. The muons from the patented muon generator have an energy of 100 MeV and above and an intensity of 1013 muons per laser pulse. Here, the detection of the relativistic laser-induced muons from H(0) is reported with a standard particle beam method, using a wire coil on a ferrite toroid as detector for the relativistic particles. The coil detection method shows that these relativistic particles are charged, thus not photons, neutrinos or neutral kaons. This makes the coil method superior to scintillator methods and it is the only possible method due to the large muon intensity. If an equal number of positive and negative mouns passed the coil, no signal would be observed. The signal at the coil in the case shown here is due to relativistic positive muons as concluded from a signal charge sign verification in the coil.

Measurement of the momentum dependence of atmospheric muon vertical intensity at ground level in Tunisia

The momentum dependence of the vertical intensity of atmospheric muons has been measured for the first time in Tunisia (region of Monastir: 35.76 N, 10.81 E) at the ground level. The measurements were conducted using a variable thickness of a lead layer placed between two NaI(Tl) scintillators allowing a selection of muons with a minimal momentum ranging from 0.3 to 1.4 GeV/c. The number of detected muons and the corresponding vertical intensity were carefully evaluated exploiting the deposited energy spectrum in the scintillators and a Monte-Carlo simulation of the experimental setup. The comparison of our results to previous measurements is satisfactory and compatible with the geomagnetic latitude dependence of the muon flux. The present measurements could improve the modelization of cosmic ray intensity at sea level by filling the lack of experimental data in North Africa.

A method to measure the integral vertical intensity and angular distribution of atmospheric muons with a stationary plastic scintillator bar detector

We present a method to measure the integral vertical intensity and angular distribution of atmospheric muons using a stationary thick plastic scintillator bar detector with PMTs at both of its ends over exposures of a few hours in a laboratory setting. The total flux is obtained from the event rate and the angular distribution is inferred from the distribution of the recorded pulse charges, which are correlated with the track length inside the plastic scintillator. A muon generator algorithm was developed and used together with a simple simulation including the effects of the detector resolution, nonlinear saturation of the PMTs, and laboratory building coverage. As a proof of principle we made a measurement assuming a standard cosnθ omnienergetic angular distribution with azimuthal isotropy and different models for the energy spectrum of the source. Using measurements at 5 different azimuthal orientations, we measure an average exponent n=(1.90±0.06(stat)±0.10(syst)), and an average vertical intensity of I0=(101.2±1.8(stat)±5.5(syst))m−2s−1sr−1 at the location with geographic coordinates 19.33°N 99.19°W, altitude 2268 m above sea level, and geomagnetic cut-off of 8.2 GV.

Beam Optics Design for the μSR Facility at the RAON Facility in Korea

The beam optics was evaluated to determine the specifications for the electromagnets in the proton beamline and the surface muon beamline at the RAON facility. Beam optics was evaluated, up to the fifth order by using GICOSY software; fringe field effects were also investigated. The distributions of the position and the angular divergence of 600-MeV protons were assumed to be Gaussian, and the initial beam emittance was 0.125 π mm mrad. The proton beamline was optimized by adjusting the positions and the magnetic fields of the electromagnetic components. The full width at half maximum (FWHM) proton beam size at the muon production target was 2.75 mm (x) × 6.73 mm (y), which met the requirement for achieving the maximum surface-muon production at the target. The designed surface-muon beamline is 23-m long and consists of two solenoids, two dipoles with a deflection angle of 70°, six quadrupoles, and a Wien filter. For an initial muon beam size of 6 cm (x) × 2 cm(y), the expected muon intensity at the end of the beamline, where the muon irradiation sample will be located, was estimated to be 7.7 × 107 per second.

MUON INTENSITY VARIATIONS AND ATMOSPHERIC TEMPERATURE

Muons in the atmosphere are formed during the decay of pions resulting from nuclear interactions of cosmic rays with nuclei of air atoms. The resulting muons are also unstable particles with a short lifetime. Therefore, not all of them reach the level of observation in the atmosphere. When the atmospheric temperature changes, the distance to the observation level changes too, thus leading to variations in the intensity of muons of temperature origin. These variations, caused by atmospheric temperature variations, are superimposed on continuous observations of muon telescopes. Their exclusion is, therefore, extremely necessary, especially in the data from modern muon telescopes whose statistical accuracy is very high. The contribution of various atmospheric layers to the total temperature effect is not the same for muons. This contribution is characterized by the distribution of the density of temperature coefficients for muons in the atmosphere. Using this distribution and the continuous intensity observations from the muon telescope in Novosibirsk, the inverse problem has been solved, from the solution of which the atmospheric temperature variations over a long period from 2004 to 2011 have been found. The results obtained are compared with aerological sounding data.

Вариации интенсивности мюонов и температура атмосферы

Muons in the atmosphere are formed during the decay of pions resulting from nuclear interactions of cosmic rays with nuclei of air atoms. The resulting muons are also unstable particles with a short lifetime. Therefore, not all of them reach the level of observation in the atmosphere. When the atmospheric temperature changes, the distance to the observation level changes too, thus leading to variations in the intensity of muons of temperature origin. These variations, caused by atmospheric temperature variations, are superimposed on continuous observations of muon telescopes. Their exclusion is, therefore, extremely necessary, especially in the data from modern muon telescopes whose statistical accuracy is very high. The contribution of various atmospheric layers to the total temperature effect is not the same for muons. This contribution is characterized by the distribution of the density of temperature coefficients for muons in the atmosphere. Using this distribution and the continuous intensity observations from the muon telescope in Novosibirsk, the inverse problem has been solved, from the solution of which the atmospheric temperature variations over a long period from 2004 to 2011 have been found. The results obtained are compared with aerological sounding data.

Variations of cosmic ray muon flux during thunderstorms as a tool for studying electric field distribution and particle production processes in the atmosphere

The recently published result of GRAPES-3 (a strong thunderstorm muon intensity change) and conclusions made on its basis by this collaboration are discussed and compared with the Baksan observations of muon variations during thunderstorms performed much earlier. It is demonstrated that generally both experiments are quite consistent as far as characteristic patterns of events are concerned, as well as conclusions about direct connection between amplitude of muon intensity disturbance and electric field strength in the atmosphere. However, the GRAPES-3 conclusion about gigavolt potentials associated with their event is doubtful and seems to contradict the fundamental limits on electric fields that can exist in the atmosphere.

Characterization of the varying flux of atmospheric muons measured with the Large Volume Detector for 24 years

The Large Volume Detector (LVD), hosted in the INFN Laboratori Nazionali del Gran Sasso, is triggered by atmospheric muons at a rate of $\sim 0.1$~Hz. The data collected over almost a quarter of century are used to study the muon intensity underground. The 50-million muon series, the longest ever exploited by an underground instrument, allows for the accurate long-term monitoring of the muon intensity underground. This is relevant as a study of the background in the Gran Sasso Laboratory, which hosts a variety of long-duration, low-background detectors. We describe the procedure to select muon-like events as well as the method used to compute the exposure. We report the value of the average muon flux measured from 1994 to 2017: $\mathrm{I_{\mu}^0 = 3.35 \pm 0.0005^{stat}\pm 0.03^{sys} \cdot 10^{-4} ~m^{-2} s^{-1}}$. We show that the intensity is modulated around this average value due to temperature variations in the stratosphere. We quantify such a correlation by using temperature data from the European Center for Medium-range Weather Forecasts: we find an effective temperature coefficient $\mathrm{\alpha_{T}} = 0.94\pm0.01^{stat} \pm0.01^{sys}$, in agreement with other measurements at the same depth. We scrutinise the spectral content of the time series of the muon intensity by means of the Lomb-Scargle analysis. This yields the evidence of a 1-year periodicity, as well as the indication of others, both shorter and longer, suggesting that the series is not a pure sinusoidal wave. Consequently, and for the first time, we characterise the observed modulation in terms of amplitude and position of maximum and minimum on a year-by-year basis.

Application of passive wedge absorbers for improving the performance of precision-science experiments

A scheme is discussed for momentum selection and momentum-spread reduction for muon-based experiments. The concept relies on placing a wedge absorber at a point along a beam transport system with nonzero dispersion. The technique has direct relevance to precision-science experiments such as the Fermilab Muon g-2 Experiment as it can enhance the muon beam intensity and therefore minimize the statistical uncertainty of the anomalous magnetic moment measurement. This paper presents a theoretical and numerical study about the orientation, material, geometrical parameters, and performance of this wedge. Results suggest a considerable increase in muon intensity for the Muon g-2 Experiment, when the optimal wedge is introduced along the beam path.

Beam commissioning of muon beamline using negative hydrogen ions generated by ultraviolet light

Abstract A muon linac is under development for the precise measurement of the muon anomalous magnetic moment ( g − 2 ) and electric dipole moment (EDM) with a reaccelerated thermal muon beam. An H − source driven by an ultraviolet light has been developed for the muon acceleration experiment. Prior to the acceleration experiment, a beamline commissioning was performed using this H− beam, since the accelerated muon intensity is very low. We successfully measured the magnetic rigidity, which is essential for identifying the accelerated muons. This H− source is capable of utilizing as a general-purpose beam source for other beamline.